A manufacturer of lightbulbs wants to produce bulbs thatlast about 700 hours but, of course, some bulbs burn outfaster than others. Let F(t) be the fraction of the company’sbulbs that burn out before t  hours, so F(t) always liesbetween 0 and 1. (a) Make a rough sketch of what you think the graph of Fmight look like.(b) What is the meaning of the derivative  r(t)  = F'(t)?(c) What is the value of ∫0∞ r(t) dt? Why?

Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter2: Functions
Section2.4: Average Rate Of Change Of A Function
Problem 4.2E: bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.
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A manufacturer of lightbulbs wants to produce bulbs that
last about 700 hours but, of course, some bulbs burn out
faster than others. Let F(t) be the fraction of the company’s
bulbs that burn out before t  hours, so F(t) always lies
between 0 and 1.

(a) Make a rough sketch of what you think the graph of F
might look like.
(b) What is the meaning of the derivative  r(t)  = F'(t)?
(c) What is the value of ∫0 r(t) dt? Why?

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